Stochastic Processes and their Applications最新文献

{"title":"On a class of exponential changes of measure for stochastic PDEs","authors":"Thorben Pieper-Sethmacher ,&nbsp;Frank van der Meulen ,&nbsp;Aad van der Vaart","doi":"10.1016/j.spa.2025.104630","DOIUrl":"10.1016/j.spa.2025.104630","url":null,"abstract":"<div><div>Given a mild solution <span><math><mi>X</mi></math></span> to a semilinear stochastic partial differential equation (SPDE), we consider an exponential change of measure based on its infinitesimal generator <span><math><mi>L</mi></math></span>, defined in the topology of bounded pointwise convergence. The changed measure <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>h</mi></mrow></msup></math></span> depends on the choice of a function <span><math><mi>h</mi></math></span> in the domain of <span><math><mi>L</mi></math></span>. In our main result, we derive conditions on <span><math><mi>h</mi></math></span> for which the change of measure is of Girsanov-type. The process <span><math><mi>X</mi></math></span> under <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>h</mi></mrow></msup></math></span> is then shown to be a mild solution to another SPDE with an extra additive drift-term. We illustrate how different choices of <span><math><mi>h</mi></math></span> impact the law of <span><math><mi>X</mi></math></span> under <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>h</mi></mrow></msup></math></span> in selected applications. These include the derivation of an infinite-dimensional diffusion bridge as well as the introduction of guided processes for SPDEs, generalizing results known for finite-dimensional diffusion processes to the infinite-dimensional case.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104630"},"PeriodicalIF":1.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Expected hitting time estimates on finite graphs","authors":"Laurent Saloff-Coste ,&nbsp;Yuwen Wang","doi":"10.1016/j.spa.2025.104626","DOIUrl":"10.1016/j.spa.2025.104626","url":null,"abstract":"<div><div>The expected hitting time from vertex <span><math><mi>a</mi></math></span> to vertex <span><math><mi>b</mi></math></span>, <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow></mrow></math></span>, is the expected value of the time it takes a random walk starting at <span><math><mi>a</mi></math></span> to reach <span><math><mi>b</mi></math></span>. In this paper, we give estimates for <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow></mrow></math></span> when the distance between <span><math><mi>a</mi></math></span> and <span><math><mi>b</mi></math></span> is comparable to the diameter of the graph, and the graph satisfies a Harnack condition. We show that, in such cases, <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow></mrow></math></span> can be estimated in terms of the volumes of balls around <span><math><mi>b</mi></math></span>. Using our results, we estimate <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow></mrow></math></span> on various graphs, such as rectangular tori, some convex traces in <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, and fractal graphs. Our proofs use heat kernel estimates.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104626"},"PeriodicalIF":1.1,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Preventing finite-time blowup in a constrained potential for reaction–diffusion equations","authors":"John Ivanhoe,&nbsp;Michael Salins","doi":"10.1016/j.spa.2025.104627","DOIUrl":"10.1016/j.spa.2025.104627","url":null,"abstract":"<div><div>We examine stochastic reaction–diffusion equations of the form <span><math><mrow><mfrac><mrow><mi>∂</mi><mi>u</mi></mrow><mrow><mi>∂</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mi>A</mi><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mi>σ</mi><mrow><mo>(</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> on a bounded spatial domain <span><math><mrow><mi>D</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>, where <span><math><mi>f</mi></math></span> models a constrained, dissipative force that keeps solutions between <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> and 1. To model this, we assume that <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mi>σ</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> are unbounded as <span><math><mi>u</mi></math></span> approaches <span><math><mrow><mo>±</mo><mn>1</mn></mrow></math></span>. We identify sufficient conditions on the growth rates of <span><math><mi>f</mi></math></span> and <span><math><mi>σ</mi></math></span> that guarantee solutions to not escape this bounded set.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104627"},"PeriodicalIF":1.1,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On strong solutions of time inhomogeneous Itô’s equations with Morrey diffusion gradient and drift. A supercritical case","authors":"N.V. Krylov","doi":"10.1016/j.spa.2025.104619","DOIUrl":"10.1016/j.spa.2025.104619","url":null,"abstract":"<div><div>We prove the existence of strong solutions of Itô’s stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Strong uniqueness is also discussed. The results are new even if there is no drift.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104619"},"PeriodicalIF":1.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Averaging principle for slow–fast systems of stochastic PDEs with rough coefficients","authors":"Sandra Cerrai ,&nbsp;Yichun Zhu","doi":"10.1016/j.spa.2025.104618","DOIUrl":"10.1016/j.spa.2025.104618","url":null,"abstract":"<div><div>This paper examines a class of slow–fast systems of stochastic partial differential equations in which the nonlinearity in the slow equation is unbounded and discontinuous. We establish conditions that guarantee the existence of a martingale solution, and we demonstrate that the laws of the slow motions are tight, with any of their limiting points serving as a martingale solution for an appropriate averaged equation. Our findings have particular relevance for systems of stochastic reaction–diffusion equations, where the reaction term in the slow equation is only continuous and has arbitrary polynomial growth.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104618"},"PeriodicalIF":1.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fluctuations of Omega-killed level-dependent spectrally negative Lévy processes","authors":"Zbigniew Palmowski ,&nbsp;Meral Şimşek ,&nbsp;Apostolos D. Papaioannou","doi":"10.1016/j.spa.2025.104617","DOIUrl":"10.1016/j.spa.2025.104617","url":null,"abstract":"<div><div>In this paper, we solve exit problems for a level-dependent Lévy process which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All identities are given in terms of new generalisations of scale functions (counterparts of the scale function from the theory of Lévy processes), which are solutions of Volterra integral equations. Furthermore, we obtain similar results for the reflected level-dependent Lévy processes. The existence of the solution of the stochastic differential equation for reflected level-dependent Lévy processes is also discussed. Finally, to illustrate our result, the probability of bankruptcy is obtained for an insurance risk process.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104617"},"PeriodicalIF":1.1,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Intersections of Poisson k-flats in hyperbolic space: Completing the picture","authors":"Tillmann Bühler,&nbsp;Daniel Hug","doi":"10.1016/j.spa.2025.104613","DOIUrl":"10.1016/j.spa.2025.104613","url":null,"abstract":"<div><div>Let <span><math><mi>η</mi></math></span> be an isometry invariant Poisson process of <span><math><mi>k</mi></math></span>-flats, <span><math><mrow><mn>0</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>d</mi><mo>−</mo><mn>1</mn></mrow></math></span>, in <span><math><mi>d</mi></math></span>-dimensional hyperbolic space. For <span><math><mrow><mi>d</mi><mo>−</mo><mi>m</mi><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mi>k</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math></span>, the <span><math><mi>m</mi></math></span>-th order intersection process of <span><math><mi>η</mi></math></span> consists of all nonempty intersections of distinct flats <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>∈</mo><mi>η</mi></mrow></math></span>. Of particular interest is the total volume <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>r</mi></mrow><mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></msubsup></math></span> of this intersection process in a ball of radius <span><math><mi>r</mi></math></span>. For <span><math><mrow><mn>2</mn><mi>k</mi><mo>&gt;</mo><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math></span>, we determine the asymptotic distribution of <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>r</mi></mrow><mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></msubsup></math></span>, as <span><math><mrow><mi>r</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, previously known only for <span><math><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow></math></span>, and derive rates of convergence in the Kolmogorov distance. Properties of the non-Gaussian limit distribution are discussed. We further study the asymptotic covariance matrix of the vector <span><math><msup><mrow><mrow><mo>(</mo><msubsup><mrow><mi>F</mi></mrow><mrow><mi>r</mi></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mo>,</mo><mo>…</mo><mo>,</mo><msubsup><mrow><mi>F</mi></mrow><mrow><mi>r</mi></mrow><mrow><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></msubsup><mo>)</mo></mrow></mrow><mrow><mo>⊤</mo></mrow></msup></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104613"},"PeriodicalIF":1.1,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimation of subcritical Galton Watson processes with correlated immigration","authors":"Yacouba Boubacar Maïnassara ,&nbsp;Landy Rabehasaina","doi":"10.1016/j.spa.2025.104614","DOIUrl":"10.1016/j.spa.2025.104614","url":null,"abstract":"<div><div>We consider an observed subcritical Galton Watson process <span><math><mrow><mo>{</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>n</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></mrow></math></span> with correlated stationary immigration process <span><math><mrow><mo>{</mo><msub><mrow><mi>ϵ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>n</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></mrow></math></span>. Two situations are presented. The first one is when <span><math><mrow><mtext>Cov</mtext><mrow><mo>(</mo><msub><mrow><mi>ϵ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>ϵ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> for <span><math><mi>k</mi></math></span> larger than some <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>: a consistent estimator for the reproduction and mean immigration rates is given, and a central limit theorem is proved. The second one is when <span><math><mrow><mo>{</mo><msub><mrow><mi>ϵ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>n</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></mrow></math></span> has general correlation structure: under mixing assumptions, we exhibit an estimator for the logarithm of the reproduction rate and we prove that it converges in quadratic mean with explicit speed. In addition, when the mixing coefficients decrease fast enough, we provide and prove a two terms expansion for the estimator. Numerical illustrations are provided.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104614"},"PeriodicalIF":1.1,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and uniqueness of SPDEs driven by nonlinear multiplicative mixed noise","authors":"Shiduo Qu,&nbsp;Hongjun Gao","doi":"10.1016/j.spa.2025.104612","DOIUrl":"10.1016/j.spa.2025.104612","url":null,"abstract":"<div><div>This paper investigates a class of stochastic partial differential equations (SPDEs) driven by standard Brownian motion and fractional Brownian motion with Hurst parameter <span><math><mrow><mi>H</mi><mo>&gt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>. We establish the existence and uniqueness of solutions for these SPDEs in sense of almost surely. We further prove that the moments of the solutions are finite. Moreover, we explore the equivalence between the integral defined by fractional derivatives and that defined by sewing lemma.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104612"},"PeriodicalIF":1.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conditional independence in stationary distributions of diffusions","authors":"Tobias Boege ,&nbsp;Mathias Drton ,&nbsp;Benjamin Hollering ,&nbsp;Sarah Lumpp ,&nbsp;Pratik Misra ,&nbsp;Daniela Schkoda","doi":"10.1016/j.spa.2025.104604","DOIUrl":"10.1016/j.spa.2025.104604","url":null,"abstract":"<div><div>Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate diffusion processes with a sparsely structured drift. Our main result gives a characterization of the conditional independence relations that hold in a stationary distribution. The result draws on a graphical representation of the drift structure and pertains to conditional independence relations that hold generally as a consequence of the drift’s sparsity pattern.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104604"},"PeriodicalIF":1.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143518982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}