Related papers: Randomized Computation of Continuous Data: Is Brow…
We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
We define a capacity C on abstract Wiener spaces and prove that, for any u with bounded variation, the total variation measure |Du| is absolutely continuous with respect to C: this enables us to extend the usual rules of calculus in many…
We investigate different notions of "computable topological base" for represented spaces. We show that several non-equivalent notions of bases become equivalent when we consider computably enumerable bases. This indicates the existence of a…
We show that polynomial-time randomness (p-randomness) is preserved under a variety of familiar operations, including addition and multiplication by a nonzero polynomial-time computable real number. These results follow from a general…
We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index $H\geq \frac12$. We show the convergence of these schemes at first and second order. The processes obtained in the limit…
The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic processwith continuous variables, and important results can be explicitly found from…
A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random polyconvex sets and show that the convergence of the…
By the sometimes so-called 'Main Theorem' of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of HYPERcomputation allow for the effective evaluation of also discontinuous…
Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…
We study Doob's martingale convergence theorem for computable continuous time martingales on Brownian motion, in the context of algorithmic randomness. A characterization of the class of sample points for which the theorem holds is given.…
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
We study a controlled version of the Bayesian sequential testing problem for the drift of a Wiener process, in which the observer exercises discretion over the signal intensity. This control incurs a running cost that reflects the resource…
We consider the Wiener sausage for a Brownian motion with a constant drift up to time $t$ associated with a closed ball. In the two or more dimensional cases, we obtain the explicit form of the expected volume of the Wiener sausage. The…
The recent analysis on noncommutative geometry, showing quantization of the volume for the Riemannian manifold entering the geometry, can support a view of quantum mechanics as arising by a stochastic process on it. A class of stochastic…
The paper considers (a) Representations of measure preserving transformations (``rotations'') on Wiener space, and (b) The stochastic calculus of variations induced by parameterized rotations $\{T_\theta w, 0 \le \theta \le \eps\}$:…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…