86,689 research outputs found
Measurability of Semimartingale Characteristics with Respect to the Probability Law
Given a c\`adl\`ag process on a filtered measurable space, we construct a
version of its semimartingale characteristics which is measurable with respect
to the underlying probability law. More precisely, let be
the set of all probability measures under which is a semimartingale. We
construct processes which are jointly measurable in time,
space, and the probability law , and are versions of the semimartingale
characteristics of under for each . This result
gives a general and unifying answer to measurability questions that arise in
the context of quasi-sure analysis and stochastic control under the weak
formulation.Comment: 37 pages; forthcoming in 'Stochastic Processes and their
Applications
Weak Solutions of Stochastic Differential Equations over the Field of p-Adic Numbers
Study of stochastic differential equations on the field of p-adic numbers was
initiated by the second author and has been developed by the first author, who
proved several results for the p-adic case, similar to the theory of ordinary
stochastic integral with respect to Levy processes on the Euclidean spaces. In
this article, we present an improved definition of a stochastic integral on the
field and prove the joint (time and space) continuity of the local time for
p-adic stable processes. Then we use the method of random time change to obtain
sufficient conditions for the existence of a weak solution of a stochastic
differential equation on the field, driven by the p-adic stable process, with a
Borel measurable coefficient.Comment: To appear in Tohoku Math.
Measurable Stochastics for Brane Calculus
We give a stochastic extension of the Brane Calculus, along the lines of
recent work by Cardelli and Mardare. In this presentation, the semantics of a
Brane process is a measure of the stochastic distribution of possible
derivations. To this end, we first introduce a labelled transition system for
Brane Calculus, proving its adequacy w.r.t. the usual reduction semantics.
Then, brane systems are presented as Markov processes over the measurable space
generated by terms up-to syntactic congruence, and where the measures are
indexed by the actions of this new LTS. Finally, we provide a SOS presentation
of this stochastic semantics, which is compositional and syntax-driven.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
Constructing Sublinear Expectations on Path Space
We provide a general construction of time-consistent sublinear expectations
on the space of continuous paths. It yields the existence of the conditional
G-expectation of a Borel-measurable (rather than quasi-continuous) random
variable, a generalization of the random G-expectation, and an optional
sampling theorem that holds without exceptional set. Our results also shed
light on the inherent limitations to constructing sublinear expectations
through aggregation.Comment: 28 pages; forthcoming in 'Stochastic Processes and their
Applications
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