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pro vyhledávání: '"60H05, 60H15"'
Using the theory of stochastic integration developed recently by the authors, in this paper we prove an It\^{o} formula for Hilbert space-valued It\^{o} processes defined with respect to a cylindrical-martingale valued measure. As part of our study,
Externí odkaz:
http://arxiv.org/abs/2407.16086
In this paper, we consider the linear evolution equation $dy(t)=Ay(t)dt+Gy(t)dx(t)$, where $A$ is a closed operator, associated to a semigroup, with good smoothing effects in a Banach space $E$, $x$ is a nonsmooth path, which is $\eta$-H\"older conti
Externí odkaz:
http://arxiv.org/abs/2404.10650
We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev (2016), to the
Externí odkaz:
http://arxiv.org/abs/2308.10374
This paper establishes the averaging method to a coupled system consisting of two stochastic differential equations which has a slow component driven by fractional Brownian motion (FBM) with less regularity $1/3< H \leq 1/2$ and a fast dynamics under
Externí odkaz:
http://arxiv.org/abs/2307.13191
We apply the averaging method to a coupled system consisting of two evolution equations which has a slow component driven by fractional Brownian motion (FBM) with the Hurst parameter $H_1> \frac12$ and a fast component driven by additive FBM with the
Externí odkaz:
http://arxiv.org/abs/2306.02030
Autor:
Fonseca-Mora, C. A.
Publikováno v:
Stoch. Anal. Appl. 42, no.4, 797-827 (2024)
Let $\Phi'$ denote the strong dual of a nuclear space $\Phi$. In this paper we introduce sufficient conditions for the convergence uniform on compacts in probability for a sequence of $\Phi'$-valued processes with continuous or c\`{a}dl\`{a}g paths.
Externí odkaz:
http://arxiv.org/abs/2303.17082
In this paper we solve a L\'evy driven linear stochastic first order partial differential equation (transport equation) understood in the canonical (Marcus) form. The solution can be obtained with the help of the method of stochastic characteristics.
Externí odkaz:
http://arxiv.org/abs/2303.00674
In this paper we prove existence and uniqueness of a mild solution to the Young equation $dy(t)=Ay(t)dt+\sigma(y(t))dx(t)$, $t\in[0,T]$, $y(0)=\psi$. Here, $A$ is an unbounded operator which generates a semigroup of bounded linear operators $(S(t))_{
Externí odkaz:
http://arxiv.org/abs/2212.14346
Autor:
Fonseca-Mora, C. A.
Publikováno v:
Stoch. Anal. Appl. 41, no. 6, 1136-1154 (2023)
Let $\Phi$ a locally convex space and $\Psi$ be a quasi-complete, bornological, nuclear space (like spaces of smooth functions and distributions) with dual spaces $\Phi'$ and $\Psi'$. In this work we introduce sufficient conditions for time regularit
Externí odkaz:
http://arxiv.org/abs/2203.03788
Publikováno v:
Electron. J. Probab. 27: 1-26 (2022)
In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, verifies a spatial linear growth condition and is componentwise non
Externí odkaz:
http://arxiv.org/abs/2112.00393