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In this paper, we study the existence and uniqueness of mild solution for a stochastic neutral partial functional integro-differential equation with delay in a Hilbert space driven by a fractional Brownian motion and with non-deterministic…

Probability · Mathematics 2018-09-11 B. Boufoussi , S. Hajji , S. Mouchtabih

In this work, we present a detailed analysis on the exact expression of the $L^2$-norm of the symmetric-Stratonovich stochastic integral driven by a multi-dimensional fractional Brownian motion $B$ with parameter $\frac{1}{4} < H <…

Probability · Mathematics 2023-09-19 Alberto Ohashi , Francesco Russo , Frederi Viens

In this note we prove an existence and uniqueness result of solution for stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2, showing also that the solution has finite moments. The…

Probability · Mathematics 2010-03-09 Mireia Besalú , Carles Rovira

We present a dynamic model for forward curves within the Heath-Jarrow-Morton framework under the Musiela parametrization. The forward curves take values in a function space H, and their dynamics follows a stochastic partial differential…

Probability · Mathematics 2025-03-14 Nils Detering , Silvia Lavagnini

In this paper we consider the controllability of certain class of non-autonomous neutral evolution stochastic functional differential equations, with time varying delays, driven by a fractional Brownian motion in a separable real Hilbert…

Probability · Mathematics 2015-04-01 E. Lakhel

Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show…

Probability · Mathematics 2007-05-23 Peter Friz , Nicolas Victoir

We explore the existence of a continuous marginal law with respect to the Lebesgue measure for each component $(X,Y,Z)$ of the solution to coupled quadratic forward-backward stochastic differential equations (QFBSDEs) {for which the drift…

Probability · Mathematics 2024-04-23 Rhoss Likibi Pellat , Olivier Menoukeu Pamen

We construct a family $I_{n_{\eps}}(f)_{t}$ of continuous stochastic processes that converges in the sense of finite dimensional distributions to a multiple Wiener-It\^o integral $I_{n}^{H}(f1^{\otimes n}_{[0,t]})$ with respect to the…

Probability · Mathematics 2010-09-17 Xavier Bardina , Khalifa Es-Sebaiy , Ciprian Tudor

Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either…

This short note is motivated by a recently discovered connection between a drift-diffusion process in $n$-dimensional Euclidean space with a divergence-free drift sampled from a stationary and isotropic Gaussian ensemble of critical scaling…

Probability · Mathematics 2026-03-20 Sefika Kuzgun , Felix Otto , Christian Wagner

In this paper we study the controllability results of impulsive neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are…

Probability · Mathematics 2016-02-19 El Hassan Lakhel

We consider a Volterra convolution equation in $\mathbb{R}^d$ perturbed with an additive fractional Brownian motion of Riemann-Liouville type with Hurst parameter $H\in (0,1)$. We show that its solution solves a stochastic partial…

Probability · Mathematics 2023-09-26 Alessandro Bondi , Franco Flandoli

We construct a higher-order gravity model including all corrections up to mass dimension six. Starting from the Jordan frame, we derive the field equations and specialize to the FLRW background, where the dynamics take the form of a…

General Relativity and Quantum Cosmology · Physics 2026-01-13 C. M. G. R. Morais , G. Rodrigues-da-Silva , L. G. Medeiros

We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to show that HJM-equations from interest rate…

Probability · Mathematics 2007-05-23 Fabrice Baudoin , Josef Teichmann

We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite-dimensional…

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2020-08-05 Xi Geng , Cheng Ouyang , Samy Tindel

Fractional Brownian motion with the Hurst parameter $H<\frac{1}{2}$ is used widely, for instance, to describe a 'rough' stochastic volatility process in finance. In this paper, we examine an Ait-Sahalia-type interest rate model driven by a…

Probability · Mathematics 2022-05-03 Emmanuel Coffie , Xuerong Mao , Frank Proske

This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional…

Computational Finance · Quantitative Finance 2026-03-16 Kevin Mott

In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional Stochastic Differential Equation (SDE) corresponding to the bulk limit of Dyson's Brownian Motion (DBM), for all $\beta\geq 1$. Our…

Probability · Mathematics 2015-11-02 Li-Cheng Tsai

In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…

Probability · Mathematics 2016-05-26 Suprio Bhar