[图书][B] Stochastic equations in infinite dimensions

G Da Prato, J Zabczyk - 2014 - books.google.com
Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

A weak solution theory for stochastic Volterra equations of convolution type

E Abi Jaber, C Cuchiero, M Larsson… - The Annals of Applied …, 2021 - projecteuclid.org
We obtain general weak existence and stability results for stochastic convolution equations
with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and …

[图书][B] Stochastic calculus via regularizations

F Russo, P Vallois - 2022 - Springer
In physics, classical analysis plays a central role. For instance in Newtonian mechanics,
thermodynamics, and electricity, many phenomena are well explained by deterministic …

Regularity of Ornstein–Uhlenbeck processes driven by a Lévy white noise

Z Brzeźniak, J Zabczyk - Potential Analysis, 2010 - Springer
The paper is concerned with spatial and time regularity of solutions to linear stochastic
evolution equation perturbed by Lévy white noise “obtained by subordination of a Gaussian …

[HTML][HTML] n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes

M Errami, F Russo - Stochastic Processes and their Applications, 2003 - Elsevier
In this paper, we introduce first a natural generalization of the concept of Dirichlet process,
providing significant examples. The second important tool concept is the n-covariation and …

[HTML][HTML] Time regularity of solutions to linear equations with Lévy noise in infinite dimensions

S Peszat, J Zabczyk - Stochastic Processes and their Applications, 2013 - Elsevier
The existence of strong and weak càdlàg versions of a solution to a linear equation in a
Hilbert space H, driven by a Lévy process taking values in a Hilbert space U↩ H is …

Time regularity of generalized Ornstein–Uhlenbeck processes with Lévy noises in Hilbert spaces

Y Liu, J Zhai - Journal of Theoretical Probability, 2016 - Springer
In this paper we first obtain a necessary condition for H H-càdlàg modification and H H-
weakly càdlàg modification of generalized Ornstein–Uhlenbeck processes with Lévy noises …

[PDF][PDF] Two results on continuity and boundedness of stochastic convolutions

S Kwapień, MB Marcus, J Rosiński - Annales de l'IHP Probabilités et …, 2006 - numdam.org
Two results on continuity and boundedness of stochastic convolutions Page 1 Ann. IH
Poincaré – PR 42 (2006) 553–566 www.elsevier.com/locate/anihpb Two results on continuity …

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

Z Brzeźniak, T Kok - Finance and Stochastics, 2018 - Springer
The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the
linear part of the drift being a generator of a C 0 C_0-semigroup) driven by an infinite …

Forward rate models with linear volatilities

M Barski, J Zabczyk - Finance and Stochastics, 2012 - Springer
The existence of solutions to the Heath–Jarrow–Morton equation of the bond market with
linear volatility and general Lévy random factor is studied. Conditions for the existence and …