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Seminar on Stochastic Analysis, Random Fields and Applications VII

Part of the Progress in Probability Book Series (volume 67)

Editors: Dalang, Robert C.; Dozzi, Marco; Russo, Francesco

DOI: 10.1007/978-3-0348-0545-2

ISBN: 978-3-0348-0544-5

Publisher: Springer Basel - Springer Journals

Jul 31, 2013

1 - 10 of 23 Chapters

LitStream

Recent Advances Related to SPDEs with Fractional Noise

Balan, Raluca M.

Pages: 3 –22

[We review the literature related to stochastic partial differential equations with spatially-homogeneous Gaussian noise, and explain how one can introduce the structure of the fractional Brownian motion into the temporal component of the noise. The Hurst parameter H is assumed to be greater than...
LitStream

On Chaos Representation and Orthogonal Polynomials for the Doubly Stochastic Poisson Process

Nunno, Giulia Di; Sjursen, Steffen

Pages: 23 –54

[In an L2-framework, we study various aspects of stochastic calculus with respect to the centered doubly stochastic Poisson process. We introduce an orthogonal basis via multilinear forms of the value of the random measure and we analyze the chaos representation property. We review the structure...
LitStream

General Upper and Lower Tail Estimates Using Malliavin Calculus and Stein’s Equations

Eden, Richard; Viens, Frederi

Pages: 55 –84

[Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati, we provide a general technique to compare the tail of a given random variable to that of a reference distribution, and apply it to all reference distributions in the so-called Pearson class. This enables us to give...
LitStream

Uniqueness and Absolute Continuity for Semilinear SPDE’s

Ferrario, Benedetta

Pages: 85 –94

[Given a weak solution of a semilinear stochastic partial differential equation, sufficient conditions for its uniqueness in law are presented. Moreover we characterize this law and prove that it is absolutely continuous with respect to the law of the process solving the corresponding linear...
LitStream

Rate of Convergence of Wong–Zakai Approximations for Stochastic Partial Differential Equations

Gyöngy, István; Stinga, Pablo Raúl

Pages: 95 –130

[In this paper we show that the rate of convergence of Wong–Zakai approximations for stochastic partial differential equations driven by Wiener processes is essentially the same as the rate of convergence of the driving processes Wn approximating the Wiener process, provided the area processes of...
LitStream

Weak Approximations for SDE’s Driven by Lévy Processes

Kohatsu-Higa, Arturo; Ngo, Hoang-Long

Pages: 131 –169

[In this article we briefly survey recent advances in some simulation methods for Lévy driven stochastic differential equations. We give a brief description of each method and extend the one jump scheme method for some subordinated models like the NIG process. Simulations of all the presented...
LitStream

Itô’s Formula for Banach-space-valued Jump Processes Driven by Poisson Random Measures

Mandrekar, Vidyadhar; Rüdiger, Barbara; Tappe, Stefan

Pages: 171 –186

[We prove Itô’s formula for a general class of functions H: ℝ+ ×F→G of class C1,2, where F,G are separable Banach spaces, and jump processes driven by a compensated Poisson random measure.]
LitStream

Well-posedness for a Class of Dissipative Stochastic Evolution Equations with Wiener and Poisson Noise

Marinelli, Carlo

Pages: 187 –196

[We prove existence and uniqueness of mild and generalized solutions to a class of stochastic semilinear evolution equations driven by additive Wiener and Poisson noise. The non-linear drift term is supposed to be the evaluation operator associated to a continuous monotone function satisfying a...
LitStream

Localization of Relative Entropy in Bose–Einstein Condensation of Trapped Interacting Bosons

Morato, Laura M.; Ugolini, Stefania

Pages: 197 –210

[We consider a system of interacting diffusions which is naturally associated to the ground state of the Hamiltonian of a system of N pairinteracting bosons and we give a detailed description of the phenomenon of the “localization of the relative entropy”. The method is based on peculiar...
LitStream

Multi-dimensional Semicircular Limits on the Free Wigner Chaos

Nourdin, Ivan; Peccati, Giovanni; Speicher, Roland

Pages: 211 –221

[We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular law is equivalent to joint convergence. This result extends to the free probability setting some findings by Peccati and Tudor (2005), and...

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