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  • 1.
    Aurzada, Frank
    et al.
    Technical University of Darmstadt, Germany .
    Dereich, Steffen
    University of Münster, Germany .
    Lifshits, Mikhail
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. St. Petersburg State University, Russia.
    Persistence probabilities for a Bridge of an integrated simple random walk2014In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 34, no 1, p. 1-22Article in journal (Refereed)
    Abstract [en]

    We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability n(-1/2) to stay positive. This question is motivated by random polymer models and proves a conjecture by Caravenna and Deuschel.

  • 2.
    Wahlberg, Patrik
    Univ Turin, Dipartimento Matemat, I-10123 Turin, TO, Italy.
    Regularization of kernels for estimation of the Wigner spectrum of Gaussian stochastic processes2010In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 30, no 2, p. 369-381Article in journal (Refereed)
    Abstract [en]

    We study estimation of the Wigner time-frequency spectrum of Gaussian stochastic processes. Assuming the covariance belongs to the Feichtinger algebra, we construct an estimation kernel that gives a mean square error arbitrarily close to the infimum over kernels in the Feichtinger algebra.

  • 3.
    Wahlberg, Patrik
    et al.
    Univ Turin, Italy.
    Schreier, Peter
    Univ Gesamthsch Paderborn, Germany.
    On the instantaneous frequency of Gaussian stochastic processes2012In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 32, no 1, p. 69-92Article in journal (Refereed)
    Abstract [en]

     We study the instantaneous frequency (IF) of continuous-time, complex-valued, zero-mean, proper, mean-square differentiable, non-stationaryGaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum.

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