Stochastic Processes and their Applications最新文献

{"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}

{"title":"Global well-posedness and enhanced dissipation for the 2D stochastic Nernst–Planck–Navier–Stokes equations with transport noise","authors":"Quyuan Lin ,&nbsp;Rongchang Liu ,&nbsp;Weinan Wang","doi":"10.1016/j.spa.2025.104603","DOIUrl":"10.1016/j.spa.2025.104603","url":null,"abstract":"<div><div>In this paper, we consider the 2D stochastic Nernst–Planck–Navier–Stokes equations incorporating transport noise affecting both momentum and ionic concentrations. By assuming the ionic species have the same diffusivity and opposite valences, we prove the global well-posedness of the system. Furthermore, we illustrate the enhanced dissipation phenomenon in the system with specific transportation noise by establishing that it enables an arbitrarily large exponential convergence rate of the solutions.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104603"},"PeriodicalIF":1.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419924","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":"The geometry of controlled rough paths","authors":"Mazyar Ghani Varzaneh ,&nbsp;Sebastian Riedel ,&nbsp;Alexander Schmeding ,&nbsp;Nikolas Tapia","doi":"10.1016/j.spa.2025.104594","DOIUrl":"10.1016/j.spa.2025.104594","url":null,"abstract":"<div><div>We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dimensional) vector bundle and allows to define a topology on the total space, the collection of all controlled path spaces, which turns out to be Polish in the geometric case. The construction is intrinsic and based on a new approximation result for controlled rough paths. This framework turns well-known maps such as the rough integration map and the Itô–Lyons map into continuous (structure preserving) mappings. Moreover, it is compatible with previous constructions of interest in the stability theory for rough integration.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104594"},"PeriodicalIF":1.1,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487789","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":"Gradual convergence for Langevin dynamics on a degenerate potential","authors":"Gerardo Barrera ,&nbsp;Conrado da-Costa ,&nbsp;Milton Jara","doi":"10.1016/j.spa.2025.104601","DOIUrl":"10.1016/j.spa.2025.104601","url":null,"abstract":"<div><div>In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed intensity, as time tends to infinity, the solution of this stochastic dynamics converges exponentially fast in total variation distance to a unique equilibrium distribution. We suitably accelerate the random dynamics and show that the preceding convergence is gradual, that is, the function that associates to each fixed <span><math><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math></span> the total variation distance between the accelerated random dynamics at time <span><math><mi>t</mi></math></span> and its equilibrium distribution converges, as the noise intensity tends to zero, to a decreasing function with values in <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>. Moreover, we prove that this limit function for each fixed <span><math><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math></span> corresponds to the total variation distance between the marginal, at time <span><math><mi>t</mi></math></span>, of a stochastic differential equation that comes down from infinity and its corresponding equilibrium distribution. This completes the classification of all possible behaviors of the total variation distance between the time marginal of the aforementioned stochastic dynamics and its invariant measure for one dimensional well-behaved convex potentials. In addition, there is no cut-off phenomenon for this one-parameter family of random processes and asymptotics of the mixing times are derived.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104601"},"PeriodicalIF":1.1,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419923","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":"Stochastic parallel translations and diffusions on the Wasserstein space over T","authors":"Hao Ding ,&nbsp;Shizan Fang ,&nbsp;Xiang-Dong Li","doi":"10.1016/j.spa.2025.104602","DOIUrl":"10.1016/j.spa.2025.104602","url":null,"abstract":"<div><div>We establish the existence and uniqueness of stochastic parallel translations and diffusions driven by a Q-Wiener process on the Wasserstein space over <span><math><mi>T</mi></math></span>. Surprisingly enough, the equation defining stochastic parallel translations is a SDE on a Hilbert space, instead of a SPDE.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104602"},"PeriodicalIF":1.1,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419922","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":"Fast exact simulation of the first-passage event of a subordinator","authors":"Jorge Ignacio González Cázares ,&nbsp;Feng Lin ,&nbsp;Aleksandar Mijatović","doi":"10.1016/j.spa.2025.104599","DOIUrl":"10.1016/j.spa.2025.104599","url":null,"abstract":"<div><div>This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. The algorithm applies to a large non-parametric class of subordinators of interest in applications. We prove that the running time of this algorithm has finite moments of all positive orders and give an explicit bound on the expected running time in terms of the Lévy measure of the subordinator. This bound provides performance guarantees that make our algorithm suitable for Monte Carlo estimation.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104599"},"PeriodicalIF":1.1,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143386638","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}